This does sound quite different from the Marhaba service, as I read it from their web site to be "Full Escort from terminal - immigration - baggage area - till meeting point"

I will know more as, out of both curiosity, and concern for a friend who will arrive from a 20 hour journey days after a minor surgical procedure, I've booked him the Marhaba service together with one of their cars to bring him to my apartment (he's traveling Business but not on EK, so doesn't already have a car).

In any case, if Marhaba deliver what their web site says, then they seem considerably more comprehensive than the EK "meet and greet" as they stay with you from the plane to the car. One of the most important things in my booking was that I wanted some continuity from arrival to transport for a friend who may not have mobile data services on arrival at 04:30 in the morning, and therefore may have issues with unexpected delays on PCR, immigration, etc. which would normally require communication with a separate driver.

I will advise in a few days how his experience was, and in comparison to my own experience arriving EK First with an escort to PCR and then being on my own until connecting with the Chauffeur Drive desk.